This invention is related to the design of optimized metalization structures and, more particularly, to modeling of electromagnetic interactions in electrical circuit metalizations to simulate the electrical properties of metalization structures in integrated circuits from their physical characteristics and using those electrical properties to obtain improved metalization performance.
It is desirable to be able to model quickly and accurately the electrical characteristics of metalization structures, such as inductors, interconnects and the like. It is also desirable to generate metalization structures that minimize the flow of unwanted signals between circuit nodes. Determination of these electrical characteristics requires a detailed solution of the charge density everywhere in the metalization structure combined with an understanding of the extent to which time dependent variations in the charge density will generate unwanted variations in the charge density elsewhere. Because of very rapid three (3) dimensional variation in charge density with position in known metalization structures and because these variations strongly affect the electrical characteristics of the metalizations and because the variations can arise from variations in distant metalization structures, an accurate and fast method for determining those charge distributions and the interactions between those charge distributions is required in order to properly determine the electrical properties of, for example, inductors or other systems of metals. One family of techniques that has been used for this purpose, employs a uniform or variable three (3) dimensional mesh of the entire metalization structure and assumes that the charge distribution will be strongly determined by interactions with adjacent metalization structures at all distances. However, these so-called long range solvers are very inefficient, i.e., slow, when employed in an attempt to model metalization structures that are largely planar as in integrated circuit metalization structures and that are strongly shielded from distant structures. Another family of techniques employs so-called short range solvers that are faster than the long range solvers, but do not account for long range interactions that may be important and, therefore, these short range solvers yield inaccurate results.
These and other problems and limitations of prior known modeling arrangements and methods are overcome by employing automatic substrate grounding and shielding generation in conjunction with a design and simulation process for modeling the charge distributions and the interactions of these charge distributions on metalization structures arising from voltages and currents flowing in metalization structures. By generating and, then, employing a grounding structure that is optimized to strongly screen the metalization structure being designed and simulated, the requirement is eliminated for the accurate incorporation of the strongly dependent long range metalization sub unit to sub unit charge distribution coupling from the charge distribution determination process.
In one embodiment of the invention, representative metalization sub units are selected, such as straight sections of infinitesimal length, right angle bends and intersections. Charge distributions are determined in those representative sub units based on the assumption that the integrated circuit substrate strongly suppresses any long range circuit interactions or frequency dependent effects. Then, based on the above assumption, self and mutual interactions are determined of the metalization sub units. Further, based on determined characteristics of those sub units, substrate grounding structures are determined and constructed that ensure the validity of the simulation assumption that the substrate grounding is adequate to strongly suppress any long range circuit interactions and/or frequency dependent effects. The determined self and mutual interactions can then be used as initial solutions to describe all interactions between similar metalization sub units in the overall physical metalization structure to be fabricated.
Technical advantages arising from use of applicant""s unique shielding arrangement are a significant reduction in the time required to obtain simulation results for modeling the metalization structures, while still maintaining a very acceptable accuracy of results, and the ability to perform the simulation process concurrently with the process of modeling the grounding structure that provides the substrate shielding.